Question

A proton and an electron have the same de Broglie wavelength. If \(K_{p}\) and \(K_{e}\) be the kinetic energies of proton and electron respectively. Then choose the correct relation :

(1) \(\mathrm{K}_{\mathrm{p}}>\mathrm{K}_{\mathrm{e}}\)

(2) \(\mathrm{K}_{\mathrm{p}}=\mathrm{K}_{\mathrm{e}}\)

(3) \(\mathrm{K}_{\mathrm{p}}=\mathrm{K}_{\mathrm{e}}{ }^{2}\)

(4) \(\mathrm{K}_{\mathrm{p}}<\mathrm{K}_{\mathrm{e}}\)  

Answer 1

Correct option is :  (4) \(\mathrm{K}_{\mathrm{p}}<\mathrm{K}_{\mathrm{e}}\)  

De Broglie wavelength of proton & electron \(=\lambda\)

\(\because\ \lambda=\frac{\mathrm{h}}{\mathrm{p}}\)

\(\therefore \ \mathrm{p}_{\text {proton }}=\mathrm{p}_{\text {electron }}\)

\(\because \ \mathrm{KE}=\frac{\mathrm{p}^{2}}{2 \mathrm{m}}\)

\(\therefore \ \mathrm{KE}_{\text {proton }}<\mathrm{KE}_{\text {electron }}\)

\(\left[\mathrm{K}_{\mathrm{p}}<\mathrm{K}_{\mathrm{e}}\right]\)